Math 242, Spring 2019, Assignment 12

From cartan.math.umb.edu

"When I think of Euclid even now, I have to wipe my sweaty brow."

- C. M. Bellman

Read:[edit]

  1. Section 15.8.
  2. Section 15.9.

Carefully define the following terms, then give one example and one non-example of each:[edit]

  1. (x,y)(u,v) (the Jacobian of the two-dimensional coordinate system (u,v)).
  2. (x,y,z)(u,v,w) (the Jacobian of the three-dimensional coordinate system (u,v,w)).
  3. ρ,θ, and ϕ (the spherical coordinates of a point in three-dimensional space).

Carefully state the following theorems (you do not need to prove them):[edit]

  1. Formula for the reduction of double integrals to iterated integrals in an arbitrary two-dimensional coordinate system (i.e. dA=).
  2. Formula for the reduction of double integrals to iterated integrals in an arbitrary three-dimensional coordinate system (i.e. dV=).
  3. Formulas to convert between rectangular and spherical coordinates.
  4. Formula for the reduction of double integrals to iterated integrals spherical coordinates (i.e. dV=).

Solve the following problems:[edit]

  1. Section 15.8, problems 1, 3, 5, 7, 9, 11, 15, 17, 19, 20, 21, 23, 25, and 41.
  2. Section 15.9, problems 1, 3, 11, 13, 15, 17, 21(a-b), and 23.
--------------------End of assignment--------------------

Questions:[edit]

Solutions:[edit]